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BEGIN:VEVENT
UID:2f9acaa5f98c1f4e6c6592c790e1ef05
CATEGORIES:Colloquia
CREATED:20260127T115046
SUMMARY:Structure preserving scientific machine learning through discrete exterior calculus
LOCATION:Hill 705
DESCRIPTION:<p>While AI and machine learning continue to make rapid progress, the ad ho
 c construction of model architectures presents major challenges for develop
 ing scientific machine learning methods that preserve the theoretical guara
 ntees underpinning conventional modeling and simulation. In this talk, we p
 resent recent work developing hybrid transformer–finite element architectur
 es that incorporate the design principles of finite element exterior calcul
 us (FEEC). Using this framework, we formulate equality-constrained optimiza
 tion problems that allow us to reverse engineer reduced-order descriptions 
 of physical systems from data while preserving topological structure. We pr
 ovide an overview of several results based on this approach: mixed finite e
 lement methods yield autoregressive models that outperform foundation model
 s with 1000× fewer parameters; metriplectic brackets preserve nonequilibriu
 m statistics in coarse-grained systems; and coordinate-free representations
  of geometry and physics produce models that remain accurate on geometries 
 unseen during training.</p>
CONTACT:Nat Trask
DTSTAMP:20260827T015801
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DTEND;TZID=America/New_York:20260313T163000
SEQUENCE:0
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